to prevent this from happening(although not fix the problem)
put the car in 1st before you turn it off,
put your foot on the brake,
come off the clutch slowly and watch the RPM's drop,
right before your engine dies turn your key to shut it off and then let out the clutch when the ignition is off,
this stop "Detonation" (keep your foot pressed down on the brake the whole time )
I had both of these problems with my car, and to a worse extent. My car would die when slowing down coming off the freeway, coming up to stop signs, you name it. Also I had the worst chugging/jerking in every gear between 2000 to 3000 rpms, and it had nothing to do with my driving (as someone above suggested).
I rebuilt my carb with this kit http://www.piercemanifolds.com/product_p/92.3237.05%20major.htm
and although it isn't exact, I followed this guidehttp://www.mk3supra.org/topic/561-guide-rebuilding-a-weber-3236-dgav-carb/ (he also talks about tuning your carb and setting the idle which is easy and vital!)
Pay careful attention to everything! And make sure you get the float 100% spot on.
After the rebuild the car drives insanely better, no jerking at any rpms, no fluctuation in the idle, everything runs smooth and sounds great.
Oh and do everything A.D.D . said. Seeing as you've only had the car a few weeks his advice will help your car run better in everyway.
Goodluck bud!